13. Formulate the following as a linear programming problem. Do not solve.

A trucking company with Rs 40,00,000 to spend on new equipment is contemplating three types of vehicles. Vehicle A has a IO-tonne pay-load and is expected to average 35 km per hour. It costs Rs 80,000. Vehicle B has a 20-tonne pay-load and is expected to average 30 km per hour. It costs Rs 1,30,000. Vehicle C is a modified form of B; it carries sleeping quarter for one driver, and this reduces its capacity to 18 tonnes and raises the cost to Rs 1,50,000. Vehicle A requires a crew of one man, and if driven on three shifts per day, could be run for an average of 18 hours per day. Vehicles B and C require a crew of two men each, but whereas B would be driven 18 hours per day with three shifts, C could average 21 hours per day. The company has 150 drivers available each day and would find it very difficult to obtain further crews. Maintenance facilities are such that the total number of vehicles must not exceed 30. How many vehicles of each type should be purchased if the company wishes to maximise its capacity in tonne-kms per day?